In this paper we presented a new approach to the Hietarinta equation (REF ). From the consideration that the Hietarinta equation possesses the property of the consistency around the cube [1]}, but does not possess the discrete symmetries of the square (REF ) we applied to it the Boll's construction developed in [2]}, [3]}, [4]}, [5]}, [6]}, [7]}. The result was a seemingly new non-autonomous, two-periodic quad-equation which we called the non-autonomous Hietarinta equation (REF ). In this sense we “reconstructed” the Hietarinta equation (REF ), since from the same single-cell equation instead of using the standard embedding (REF ) we adopted a different one resulting in a different equation on the \(\mathbb {Z}^{2}\)  lattice.
